Suppose \(X_1, X_2, \ldots \)  are independent and identically distributed (i.i.d.) random variables with mean \(\mu \)  and finite positive variance \(\sigma ^2\) . The version of the central limit theorem attributed to Lévy and Lindeberg [1]} asserts that the sequence of random variables \((Y_n-n\mu )/(\sigma \sqrt{n})\)  converge in distribution to a standard normal. A theorem attributed to Lyapunov [1]} shows the assumption that the variables \(X_1, X_2, \ldots \)  be identically distributed can even be relaxed as long as the absolute moments of the \(X_i\)  satisfy a certain (Lyapunov) growth condition.
